## TPTP Problem File: SEV024^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV024^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from EQUIVALENCE-RELATIONS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1095 [Bro09]

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   44 (   2 equality;  42 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   39 (   0   ~;   0   |;   9   &;  23   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   17 (   0 sgn;  12   !;   4   ?;   1   ^)
%                                         (  17   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          : May require description or choice.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM262_pme,conjecture,(
! [P: ( a > \$o ) > \$o] :
( ( ! [Xp: a > \$o] :
( ( P @ Xp )
=> ? [Xz: a] :
( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > \$o] :
( ( P @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > \$o] :
( ( ( P @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) ) )
=> ? [Q: a > a > \$o] :
( ! [Xx: a] :
( Q @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( Q @ Xx @ Xy )
=> ( Q @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Q @ Xx @ Xy )
& ( Q @ Xy @ Xz ) )
=> ( Q @ Xx @ Xz ) )
& ( ( ^ [Xs: a > \$o] :
( ? [Xz: a] :
( Xs @ Xz )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ! [Xy: a] :
( ( Xs @ Xy )
<=> ( Q @ Xx @ Xy ) ) ) ) )
= P ) ) ) )).

%------------------------------------------------------------------------------
```